
2.7.33 Function properties
condition: Let us define the mapping \[ f: \mathbb{R}^{2} \rightarrow \mathbb{R}, \quad f(x, y)=\frac{x^{2}-|y|}{x^{2}+y^{2}} \] when \( (x, y) \neq(0,0) \) and for \( f(0,0)=0 \). At what points is the function differentiable?